**Mixed-Signal Neuromorphic
CMOL Circuits (“CrossNets”)**

**Summary:**

The CMOL circuit fabric is uniquely suitable for the
implementation of neuromorphic networks (“CrossNets”) in which cell
somas are realized the CMOS subsystem, crossbar nanowires play the roles of
axons and dendrites, and crosspoint latching switches serve as elementary
(binary-weight) synapses. The important advantage of this topology is the
possibility to implement arbitrary cell connectivity (e.g., ~10^{4}
typical for the mammal cortex) in quasi-2D electronic circuits. We have shown
that the binary character of the elementary synapses and a relatively high
defect density (possible at the initial stage of CMOL technology development) do
not prevent CrossNets from performing essentially all the tasks demonstrated
earlier with software-implemented neuromorphic networks, including
auto-association [8], pattern classification [9-11, 14], and dynamic control in
conditions of instant and delayed reward [12, 13]. The significance of these
results is in the very high potential areal density of CMOL CrossNets (beyond
that of the mammal cerebral cortex, at similar connectivity), and the very high
operation speed of these networks – e.g., intercell latency below 1
microsecond at readily manageable power dissipation below 1 W/cm^{2}
[5, 8]. We believe that CMOL CrossNets is the first hardware which may
eventually challenge the human cortex. At a shorter time scale, such circuits
may become an important tool for cortical circuit modeling.

**Publications:**

1. S. Fölling, Ö. Türel, and K. K.
Likharev,
"Single-Electron Latching Switches as Nanoscale
Synapses", in: *Proc. IJCNN’01Neural Networks,* pp. 216-221
(2001).

2. Ö.
Türel and K. K. Likharev, "CrossNets: Possible Neuromorphic Networks based on Nanoscale
Components", *Int. J. of Circuit
Theory and Applications* **31**, pp. 37-52 (2003).

3. Ö.
Türel and K. K. Likharev, "CrossNets: Neuromorphic Networks for Nanoelectronic
Implementation", *Lecture Notes
on Computer Science* **2714, **pp. 753-760 (2003).

4. Ö.
Türel, *Proc.
IJCNN’03, * pp. 365-370 (2003).

5. K. Likharev, A.
Mayr, *Ann. *.

6. Ö. Türel, J. H. Lee, X. Ma, and K. K. Likharev, "Architectures for Nanoelectronic Implementation of Artificial Neural Networks: New Results",

7. Ö. Türel, J. H. Lee, X. Ma, and K. K. Likharev,

8. Ö. Türel, J. H. Lee, X. Ma, and K. K. Likharev, "Neuromorphic Architectures for Nanoelectronic Circuits",

9. J. H. Lee and K. K. Likharev, "CMOL CrossNets as Pattern Classifiers",

10. J. H.
Lee, X. Ma, and K. K. Likharev, "CMOL CrossNets:
Possible Neuromorphic Nanoelectronic Circuits", in: *Advances in Neural Information Processing
Systems 18*, ed. by Y. Weiss *et al*.,
MIT Press, Cambridge, MA, pp. 755-762 (2006).

11. J. H. Lee and K. K.
Likharev, "In Situ Training of CMOL CrossNets", in: *Proc.* *WCCI/IJCNN’06*, pp. 5026-5034 (2006).

12.
X. Ma and K. K. Likharev, "Global Reinforcement
Learning in Neural Networks with Stochastic Synapses", in: *Proc.* *WCCI/IJCNN’06*, pp. 47-53 (2006).

13.
X. Ma and K. K. Likharev, "Global Reinforcement
Learning in Stochastic Neural Networks", *IEEE Trans. on Neural Networks* **18**,
pp. 573-577 (2007).

14.
J. H. Lee and K. K. Likharev, "Defect-Tolerant
Nanoelectronic Pattern Classifiers", *Int. J. of Circuit
Theory and Applications ***35**, pp. 239-264 (2007).

15. K. K.
Likharev, "CrossNets: Neuromorphic Hybrid
CMOS/Nanoelectronic Networks", *Science of Advanced Materials ***3**, pp. 322-331 (2011).

16. T. J. Walls and K. K.
Likharev, "Self-organization in Autonomous,
Recurrent, Firing-Rate CrossNets with Quasi-Hebbian Plasticity", *IEEE Trans. on Neural Networks and Learning
Systems*, **25**, pp. 819-824 (2014).

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